MEN OF 3IATHE3IATICS of algebra advocated by his British contemporaries, Hamilton sought to found algebra on something 'more reaF, and for this strictly meaningless enterprise he drew on his knowledge of Kant's mistaken notions - exploded by the creation of non- Euclidean geometry - of space as "a pure form of sensuous intuition'. Indeed Hamilton, who seems to have been unac- quainted with non-Euclidean geometry, followed Kant in believing that 'Time and space are two sources of knowledge from which various a priori synthetical cognitions can be derived. Of this, pure mathematics gives a splendid example in the case of our cognition of space and its various relations. As they are both pure forms of sensuous intuition, they render synthetic propositions a priori possible/ Of course any not utterly illiterate mathematician to-day knows that Kant was mistaken in this conception of mathematics, but in the 1840*s, when Hamilton was on his way to quaternions, the Kantian philosophy of mathematics still made sense to those - and they were nearly all - who had never heard of Lobatchewsky. By what looks like a bad mathematical pun, Hamilton applied the Kantian doctrine to algebra and drew the remarkable conclu- sion that, since geometry is the science of space, and since time- and space are "pure sensuous forms of intuition', therefore the rest of mathematics must belong to time, and he wasted much of his own time in elaborating the bisarre doctrine that algebra is the science of pure time. This queer crotchet has attracted many philosophers, and quite recently it has been exhumed and solemnly dissected by owlish metaphysicians seeking the philosopher's stone in the gall bladder of mathematics. Just because 'algebra as the science of pure time' is of no earthly mathematical significance, it will continue to be discussed with animation till tune itself ends. The opinion of a great mathematician on the 'pure time' aspect of algebra may be of interest. "I cannot myself recognize the connexion of algebra with the notion of tune,' Cayley con- fessed; 'granting that the notion of continuous progression prestnts itself and is of importance, I do not see that it is in any wise the fundamental notion of the science.9 Hamilton's difficulties in trying to construct an algebra of 394.